A device of this type is known from EP 1 117 488 B1; this device, however, comprises two chambers in the applicator head, which can be subjected to different pressures. The pressure p0 prevails in a prechamber, whereas the pressure p1 can be set to the desired value in the main chamber in that a sealing element is provided between the prechamber and the main chamber to separate the two chambers from each other. Toward the outside, each chamber if sealed off by a doctor blade, which presses against an associated gravure cylinder. In addition, both the main chamber and the prechamber are provided with an inlet for the free-flowing medium to be applied to the web.